A kind of problems appearing under identification of stochastic systems and concerned with applying nonlinear measures of dependence of random values (processes) is analyzed. Approaches using such a consistent measure of dependence as the Shannon's mutual information are considered. A constructive procedure of deriving a linear input/output model which is statistically equivalent to a multi input / multi output dynamic stochastic system driven by a white-noise Gaussian process is proposed. A key issue of such a procedure is using the condition of component-wise coincidence of the mutual information of the input and output processes of the system and the input and output processes of the model as an identification criterion. The approach enables one to derive explicit relationships determining elements of the weighting matrices of the linearized model. At that, using such an unreal preliminary assumption as a known joint probability distribution of the system and model output processes is eliminated.